/*-
*
* * Copyright 2015 Skymind,Inc.
* *
* * Licensed under the Apache License, Version 2.0 (the "License");
* * you may not use this file except in compliance with the License.
* * You may obtain a copy of the License at
* *
* * http://www.apache.org/licenses/LICENSE-2.0
* *
* * Unless required by applicable law or agreed to in writing, software
* * distributed under the License is distributed on an "AS IS" BASIS,
* * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* * See the License for the specific language governing permissions and
* * limitations under the License.
*
*
*/
package org.nd4j.linalg.dimensionalityreduction;
import org.nd4j.linalg.api.ndarray.INDArray;
import org.nd4j.linalg.factory.Nd4j;
/**
* PCA class for dimensionality reduction
*
* @author Adam Gibson
*/
public class PCA {
private PCA() {}
/**
* Calculates pca vectors of a matrix, for a fixed number of reduced features
* returns the reduced feature set
* The return is a projection of A onto principal nDims components
*
* To use the PCA: assume A is the original feature set
* then project A onto a reduced set of features. It is possible to
* reconstruct the original data ( losing information, but having the same
* dimensionality )
*
* <pre>
* {@code
*
* INDArray Areduced = A.mmul( factor ) ;
* INDArray Aoriginal = Areduced.mmul( factor.transpose() ) ;
*
* }
* </pre>
*
* @param A the array of features, rows are results, columns are features - will be changed
* @param nDims the number of components on which to project the features
* @param normalize whether to normalize (adjust each feature to have zero mean)
* @return the reduced parameters of A
*/
public static INDArray pca(INDArray A, int nDims, boolean normalize) {
INDArray factor = pca_factor(A, nDims, normalize);
return A.mmul(factor);
}
/**
* Calculates pca factors of a matrix, for a fixed number of reduced features
* returns the factors to scale observations
*
* The return is a factor matrix to reduce (normalized) feature sets
*
* @see pca(INDArray, int, boolean)
*
* @param A the array of features, rows are results, columns are features - will be changed
* @param nDims the number of components on which to project the features
* @param normalize whether to normalize (adjust each feature to have zero mean)
* @return the reduced feature set
*/
public static INDArray pca_factor(INDArray A, int nDims, boolean normalize) {
if (normalize) {
// Normalize to mean 0 for each feature ( each column has 0 mean )
INDArray mean = A.mean(0);
A.subiRowVector(mean);
}
int m = A.rows();
int n = A.columns();
// The prepare SVD results, we'll decomp A to UxSxV'
INDArray s = Nd4j.create(m < n ? m : n);
INDArray VT = Nd4j.create(n, n, 'f');
// Note - we don't care about U
Nd4j.getBlasWrapper().lapack().gesvd(A, s, null, VT);
// for comparison k & nDims are the equivalent values in both methods implementing PCA
// So now let's rip out the appropriate number of left singular vectors from
// the V output (note we pulls rows since VT is a transpose of V)
INDArray V = VT.transpose();
INDArray factor = Nd4j.create(n, nDims, 'f');
for (int i = 0; i < nDims; i++) {
factor.putColumn(i, V.getColumn(i));
}
return factor;
}
/**
* Calculates pca reduced value of a matrix, for a given variance. A larger variance (99%)
* will result in a higher order feature set.
*
* The returned matrix is a projection of A onto principal components
*
* @see pca(INDArray, int, boolean)
*
* @param A the array of features, rows are results, columns are features - will be changed
* @param variance the amount of variance to preserve as a float 0 - 1
* @param normalize whether to normalize (set features to have zero mean)
* @return the matrix representing a reduced feature set
*/
public static INDArray pca(INDArray A, double variance, boolean normalize) {
INDArray factor = pca_factor(A, variance, normalize);
return A.mmul(factor);
}
/**
* Calculates pca vectors of a matrix, for a given variance. A larger variance (99%)
* will result in a higher order feature set.
*
* To use the returned factor: multiply feature(s) by the factor to get a reduced dimension
*
* INDArray Areduced = A.mmul( factor ) ;
*
* The array Areduced is a projection of A onto principal components
*
* @see pca(INDArray, double, boolean)
*
* @param A the array of features, rows are results, columns are features - will be changed
* @param variance the amount of variance to preserve as a float 0 - 1
* @param normalize whether to normalize (set features to have zero mean)
* @return the matrix to mulitiply a feature by to get a reduced feature set
*/
public static INDArray pca_factor(INDArray A, double variance, boolean normalize) {
if (normalize) {
// Normalize to mean 0 for each feature ( each column has 0 mean )
INDArray mean = A.mean(0);
A.subiRowVector(mean);
}
int m = A.rows();
int n = A.columns();
// The prepare SVD results, we'll decomp A to UxSxV'
INDArray s = Nd4j.create(m < n ? m : n);
INDArray VT = Nd4j.create(n, n, 'f');
// Note - we don't care about U
Nd4j.getBlasWrapper().lapack().gesvd(A, s, null, VT);
// Now convert the eigs of X into the eigs of the covariance matrix
for (int i = 0; i < s.length(); i++) {
s.putScalar(i, Math.sqrt(s.getDouble(i)) / (m - 1));
}
// Now find how many features we need to preserve the required variance
// Which is the same percentage as a cumulative sum of the eigenvalues' percentages
double totalEigSum = s.sumNumber().doubleValue() * variance;
int k = -1; // we will reduce to k dimensions
double runningTotal = 0;
for (int i = 0; i < s.length(); i++) {
runningTotal += s.getDouble(i);
if (runningTotal >= totalEigSum) { // OK I know it's a float, but what else can we do ?
k = i + 1; // we will keep this many features to preserve the reqd. variance
break;
}
}
if (k == -1) { // if we need everything
throw new RuntimeException("No reduction possible for reqd. variance - use smaller variance");
}
// So now let's rip out the appropriate number of left singular vectors from
// the V output (note we pulls rows since VT is a transpose of V)
INDArray V = VT.transpose();
INDArray factor = Nd4j.create(n, k, 'f');
for (int i = 0; i < k; i++) {
factor.putColumn(i, V.getColumn(i));
}
return factor;
}
}